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  <H1>p<i>K</i><sub>a</sub> Calculation

</H1>

<OL>

<LI><A HREF="#Intro">Introduction</A></LI>
<LI><A HREF="#DefofKa">Definition of Acid Dissociation Constant <i>K</i><SUB>a</SUB></A></LI>
<LI><A HREF="#DefofpKa">Definition of  p<i>K</i><SUB>a</SUB></A></LI>		
<LI><A HREF="#DefofAcidBasicPrefix">Definition of acidic and basic prefix of p<i>K</i><SUB>a</SUB></A></LI>
<LI><A HREF="#MultiProtic">Multiprotic Molecules</A></LI>
<LI><A HREF="#AH3">Ionization Steps of the AH<SUB>3</SUB> Molecule</A></LI>
<LI><A HREF="#Examples">Examples</A></LI>
  	  <UL>
	          <LI><A HREF="#Example1">Example 1</A></LI>
	          <UL>
	                 <LI><A HREF="#pamSteps">Micro Ionization Steps of P-amino Benzoic Acid</A></LI>
	                 <LI><A HREF="#pampKa">Calculated and Observed p<i>K</i><SUB>a</SUB> of P-amino Benzoic Acid</A></LI>
	         </UL>
	  <LI><A HREF="#amide">Example 2</A></LI>
	  <LI><A HREF="#Example3">Example 3</A></LI>
	  </UL>
<LI><A HREF="#references">References</A></LI>

</OL>

<H2><A class="anchor" NAME="Intro" >1. Introduction</A></H2>


<p>Chemical properties of molecules depend largely on whether they are ionized or not.
 Most  organic molecules are capable of gaining and/or losing a proton in aqueous solutions. 
Proton transfer most frequently occurs between water and any ionizable atom of the organic molecule.
The molecule's response to protonation or deprotonation depends significantly on the site that was disturbed by proton transfer. 
Partial charge distribution in the molecule also varies with protonation of the acid/base active sites. 
Since the partial charge distribution is very sensitive to the protonation-deprotonation process 
(both near and far from the disturbed site), it can be used to determine the p<i>K</i><SUB>a</SUB> of a molecule.
Our p<i>K</i><SUB>a</SUB> prediction program is based on the calculation of partial charge of atoms in the molecule.<p> 


<H2>
<A class="anchor" NAME="DefofKa">
2. Definition of Acid Dissociation Constant <i>K</i><SUB>a</SUB></A>
</H2>

<p>Acidic and basic molecules are ionized in
aqueous solution.   Acidic or basic character is assigned to the molecule according to Br&#246;nsted's rule.  The ratio of the ionized and neutral forms depends on the
pH, the temperature and the ion activity of the bulk phase.
The ionization constant K<sub>a</sub> is obtained from the activity ratio of conjugated base and conjugated acid multiplied with proton activity.</p> 
<P>
<IMG SRC="pKa_files/Ka_def.gif" HSPACE=18 VSPACE=10 >
</p>

<H2>
<A class="anchor" NAME="DefofpKa">
3. Definition of  p<i>K</i><SUB>a</SUB></A>
</H2>

p<i>K</i><SUB>a</SUB> is obtained from the ionization constant of a molecule using the following definition.
<BR><BR>
<IMG SRC="pKa_files/pKa_def.gif" HSPACE=18 VSPACE=10 >
<BR><BR>
When the pH of the solution is equal with p<i>K</i><SUB>a</SUB>,  the concentrations of dissociated and undissociated species are equal.

<BR> 								 

<H2>
<A class="anchor" NAME="DefofAcidBasicPrefix">	 
4. Definition of  the acidic/basic prefix of p<i>K</i><SUB>a</SUB></A>	
</H2>
  
   <B><i>definition of the basic prefix</i></B><BR>
   Protonated positive ions are considered as <i>protonated basic sites</i> , therefore , "basic" prefix is used for them.<BR> 
   Type of the <i>neutral basic sites</i> are predefined in the p<i>K</i><SUB>a</SUB> calculator, they also have "basic" prefix.
   <BR>
   e.g.: if submitted molecule is CH<SUB>3</SUB>NH<SUB>2</SUB> or CH<SUB>3</SUB>NH<SUB>3</SUB><SUP>+</SUP> they  get "basic" prefix and p<i>K</i><SUB>a</SUB>=10.08
   
   <BR>
   <BR>
   <B><i>definition of the acidic prefix</i></B><BR>
   Deprotonated negative ions are considered as <i>deprotonated acidic sites</i> , therefore , "acidic" prefix is used for them.<BR>  
   Type of the <i>neutral acidic sites</i> are predefined in the p<i>K</i><SUB>a</SUB> calculator, they also have "acidic" prefix.
   <BR>
   e.g.: if submitted molecule is CH<SUB>3</SUB>COOH or CH<SUB>3</SUB>COO<SUP>-</SUP> they  get "acidic" prefix and p<i>K</i><SUB>a</SUB>=4.54
   
   
   



<H2>
<A class="anchor" NAME="MultiProtic">
5. Multiprotic Molecules</A>
</H2>

When a molecule contains more than one ionizable atom, it is called a multiprotic compound.
For these types of molecules we need to distinguish between micro and macro acidic dissociation constants.
The micro acidic dissociation constant is obtained from the equilibrium concentration of the conjugated acid-base pairs.
The macro acidic dissociation constant is obtained from the global mass and charge conservation  law.
When a molecule has N ionizable sites, the total number of micro species in the solution is 2<SUP>N</SUP>.
<P>
To further understand the difference between micro and macro constants
 we consider ionization equilibrium of a triprotic acid AH<SUB>3</SUB>. 
Referring to the different deprotonation sites of the AH<SUB>3</SUB> molecule we introduce the upper indexes of the protons.
<BR>
<IMG SRC="pKa_files/AH3.gif"  BORDER=0  HSPACE=18 VSPACE=10 >
<BR>
The ionization process of the AH<SUP>1</SUP>H<SUP>2</SUP>H<SUP>3</SUP> molecule in aqueous solution is described with 12 
equilibrium reactions. Micro species and their charge are summarized in <A HREF="#TABLE1">Table 1.</A>

</P>
<H2>
<A class="anchor" NAME="AH3">
6. Ionization Steps of the AH<SUB>3</SUB> Molecule</A>
</H2>

<IMG SRC="pKa_files/AH3_ions.gif"  BORDER=0  HSPACE=18 VSPACE=10 >
<BR>

<A NAME="TABLE1"></A>
Table 1. Protonation State of Microspecies
<BR>

<TABLE BORDER=1 WIDTH=50% HEIGHT=25% >

<TR><TD ><CENTER>Microspecies</CENTER></TD>
<TD><CENTER>charge</CENTER></TD>

<TR><TD><CENTER>
AH<SUP>1</SUP>H<SUP>2</SUP>H<SUP>3</SUP></CENTER></TD>
<TD><CENTER>0</CENTER></TD>

<TR><TD><CENTER>
  AH<SUP>1</SUP>H<SUP>2</SUP>
, AH<SUP>1</SUP>H<SUP>3</SUP>
, AH<SUP>2</SUP>H<SUP>3</SUP></CENTER></TD>
<TD><CENTER>-1</CENTER></TD>


<TR><TD><CENTER>
  AH<SUP>1</SUP>
, AH<SUP>2</SUP>
, AH<SUP>3</SUP>
</CENTER></TD>
<TD><CENTER>-2</CENTER></TD>

<TR><TD><CENTER>A</CENTER></TD>
<TD><CENTER>-3</CENTER></TD>

</TABLE>
<BR>
The AH<SUB>3</SUB> molecule has three macro acidic constants since it is triprotic acid. 
Macro acidic constants <i>K<SUB>1</SUB>, K<SUB>2</SUB>, </i>and <i>K<SUB>3</SUB></i> 
are obtained from the concentration of the microspecies:
<p>
  <IMG SRC="pKa_files/Macro_K.gif"  BORDER=0 VSPACE="18" HSPACE="0">
</p>
And the three macro p<i>K</i><SUB>a</SUB>  values of the AH<SUB>3</SUB> molecule that would be obtained with routine laboratory measurements are as follows:
<BR><BR>
p<i>K</i><SUB>a,1</SUB>=-log<SUB>10</SUB>(<i>K</i><SUB>1</SUB>)
<BR>
p<i>K</i><SUB>a,2</SUB>=-log<SUB>10</SUB>(<i>K</i><SUB>2</SUB>)
<BR>
p<i>K</i><SUB>a,3</SUB>=-log<SUB>10</SUB>(<i>K</i><SUB>3</SUB>)
<BR>

<H2>
<A class="anchor" NAME="Examples">
7. Examples</A>
</H2>

<A NAME="Example1"></A>
<B>Example 1.</B>
<BR><BR>
The ionization steps of <i>p</i>-amino benzoic acid are outlined below. Calculated micro 
ionization constants <i>k<SUB>1</SUB>, k<SUB>2</SUB>, k<SUB>3</SUB></i> 
and <i>k<SUB>4</SUB></i> are indicated on the arrows:
<BR>
<A NAME="pamSteps"></A>
<IMG width="450" height="438" SRC="pKa_files/pAm_k.png">
<BR>
<A NAME="pampKa"></A>
Below are the calculated and the experimental p<i>K</i><SUB>a</SUB> of  <i>p</i>-amino benzoic acid
<BR>
<IMG SRC="pKa_files/pKa12.png" WIDTH="193" HEIGHT="60">
<BR><BR>
<A NAME="amide"></A>
<B>Example 2.</B>
<BR><BR>
 Imides and amides can have either acidic or  basic character.
The extent of amide/imide ionization at a given pH is determined by two acid dissociation constants:
<BR><BR>
p<i>K</i><SUB>a,1</SUB>assigned to the deprotonation step
<BR>
RNH <IMG align="absbottom" SRC="pKa_files/reactionarrow.png" WIDTH="39" HEIGHT="19"> RN<SUP>-</SUP> + H<SUP>+</SUP>
<BR><BR>
and 
p<i>K</i><SUB>a,2</SUB>assigned to the protonation step
<BR>
RNH<SUB>2</SUB><SUP>+</SUP> <IMG align="absbottom" SRC="pKa_files/reactionarrow.png" WIDTH="39" HEIGHT="19">RNH + H<SUP>+</SUP>
<BR><BR>
Ratio of anionic and cationic species depends on p<i>K</i><SUB>a,1</SUB>, p<i>K</i><SUB>a,2</SUB> and the pH:
<BR><BR>
<IMG SRC="pKa_files/amide_ratio.gif"  BORDER=0   HSPACE=18 VSPACE=10 WIDTH="166" HEIGHT="38">
<BR><BR>
If 2pH - (p<i>K</i><SUB>a,1</SUB> + p<i>K</i><SUB>a,2</SUB>) &gt; 0 than deprotonation of amide/imide is favored and the molecule is said to have an acidic character.
<BR>
If 2pH - (p<i>K</i><SUB>a,1</SUB> + p<i>K</i><SUB>a,2</SUB>) &lt; 0 than protonation  of amide/imide is favored and it is considered to have a basic character.
<BR><BR>

Chemists often want to know the ionization state of organic compounds at pH 7.4.  
In general, the macro p<i>K</i><SUB>a</SUB>s of amide/imide compounds are calculated and their acidic 
or basic character determined with the above formulas at pH 7.4.
<BR><BR>
Calculated and measured p<i>K</i><SUB>a</SUB> of phtalimide and 2-pyridone are given in 
Table 2.
<IMG SRC="pKa_files/phtal.jpg" WIDTH="324" HEIGHT="151">
<p>

Table 2. Calculated and Observed Acidity Constants
<TABLE BORDER=1 WIDTH=50%  HEIGHT=15%>

<TR><TD ><CENTER>Compound</CENTER></TD>
<TD><CENTER>Calculated p<i>K</i><SUB>a</SUB></CENTER></TD>
<TD><CENTER>Observed p<i>K</i><SUB>a</SUB></CENTER></TD>

<TR><TD><CENTER>phtalimide</CENTER></TD>
<TD><CENTER><FONT  COLOR="RED">8.22</FONT></CENTER></TD>
<TD><CENTER><FONT  COLOR="RED">8.30</FONT></CENTER></TD>

<TR><TD><CENTER>2-pyridone</CENTER></TD>
<TD><CENTER><FONT  COLOR="RED">11.40</FONT></CENTER></TD>
<TD><CENTER><FONT  COLOR="RED">11.70</FONT></CENTER></TD>

</TABLE></p>

<BR><BR>
<A NAME="Example3"></A>
<B>Example 3</B>
<P>The value of ionization constants of conjugated acid-base pairs 
usually falls between 10<SUP>-10</SUP> and 10<SUP>20</SUP>, so
 these limits are generally used to predict the p<i>K</i><SUB>a</SUB>.

When an ionizable site in the molecule has very weak basic or acidic character, this can be accomodated by increasing the calculation range.
<BR><BR>
The molecule depicted below contains a very weak basic atom.
First, macro p<i>K</i><SUB>a</SUB> is calculated  with  default limits predefined between 
10<SUP>-10</SUP> and 10<SUP>20</SUP>.
Then  macro p<i>K</i><SUB>a</SUB> is calculated with altered limits defined between 
10<SUP>-50</SUP> and 10<SUP>20</SUP>.
<BR>
Changing of the default settings of macro p<i>K</i><SUB>a</SUB> calculation can be done in the 
Tools <IMG align="absbottom" SRC="pKa_files/arrow.gif" WIDTH="15" HEIGHT="9"> Options <IMG align="absbottom" SRC="pKa_files/arrow.gif"  WIDTH="15" HEIGHT="9"> p<i>K</i><SUB>a</SUB> menu of MarvinSketch.
<BR>
Calculated and observed acidity constants are summarized in Table 3. Measured p<i>K</i><SUB>a</SUB>s taken from <A HREF="#ref3">Ref.3.</A> 
<BR><BR>
<IMG SRC="pKa_files/limits.jpg"  BORDER=0  HSPACE=18 VSPACE=10 WIDTH="579" HEIGHT="309">
<BR><BR><BR>
<A NAME="Table3"></A>
Table 3. Calculated and Observed Acidity Constants
<TABLE BORDER=1 WIDTH=55%  HEIGHT=20%>

<TR><TD ><CENTER>p<i>K</i><SUB>a</SUB></CENTER></TD>
<TD><CENTER>First calc.</CENTER></TD>
<TD><CENTER>Second calc.</CENTER></TD>
<TD><CENTER>Observed</CENTER></TD>

<TR><TD ><CENTER><FONT  COLOR="RED">p<i>K</i><SUB>a,1</SUB></FONT></CENTER></TD>
<TD><CENTER><FONT COLOR="RED">4.24</FONT></CENTER></TD>
<TD><CENTER><FONT  COLOR="RED">4.24</FONT></CENTER></TD>
<TD><CENTER><FONT  COLOR="RED">4.51</FONT></CENTER></TD>

<TR><TD ><CENTER><FONT  COLOR="BLUE">p<i>K</i><SUB>a,2</SUB></FONT></CENTER></TD>
<TD><CENTER><FONT COLOR="BLUE">5.75</FONT></CENTER></TD>
<TD><CENTER><FONT  COLOR="BLUE">5.75</FONT></CENTER></TD>
<TD><CENTER><FONT COLOR="BLUE">6.01</FONT></CENTER></TD>

<TR><TD ><CENTER><FONT COLOR="BLUE">p<i>K</i><SUB>a,3</SUB></FONT></CENTER></TD>
<TD><CENTER><FONT  COLOR="BLUE">-</FONT></CENTER></TD>
<TD><CENTER><FONT  COLOR="BLUE">-35.81</FONT></CENTER></TD>
<TD><CENTER><FONT  COLOR="BLUE">-</FONT></CENTER></TD>


</TABLE>
<BR><BR>



<H2>
<A class="anchor" NAME="references">
8. References</A>
</H2>
<OL>
<LI>Dixon, S. L.; Jurs, P. C., <i>J. Comp. Chem.</i>, <b>1993</b>, <i>14</i>, 12, 1460-1467; <a href="http://dx.doi.org/10.1002/jcc.540141208">doi</a></LI>
<LI>Csizmadia, F.; Tsantili-Kakoulidou, A.; Panderi, I.; Darvas, F., <i>J. Pharm. Sci.</i>, <b>1997</b>, <i>86</i>, 7, 865-871; <a href="http://dx.doi.org/10.1021/js960177k">doi</a></LI>
<LI><A class="text" NAME="ref3">Clark, F. H.; Cahoon, N. M., <i>J. Pharm. Sci.</i>, <b>1987</b>, <i>76</i>, 8, 611-620</A></LI>

</OL>


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